Rheonomous constraint

Remarks

Example: a pendulum of length $\ell > 0$ whose pivot moves on the vertical axis as $p(t) = (0, 0, a \cos(\omega t))$, with $a \ne 0$ and $\omega \ne 0$, obeys $\abs{x - p(t)}^2 - \ell^2 = 0$, and this function depends on $t$. Non-example: the same pendulum with a fixed pivot obeys $\abs{x}^2 - \ell^2 = 0$, which has no explicit $t$. Whether a constraint is rheonomous can depend on the coordinates. In a frame that rotates with a turning wire, the constraint of a bead on the wire no longer contains $t$, but that frame is not inertial.